obstacle
碍 centers on something that blocks or hinders progress: an obstacle that stands in the way.
碍 is the modern simplified form of 礙. The older form combines 石 (stone) with 疑, which likely contributed the sound and the idea of something that blocks or hinders. The modern right-side component 㝵 is a simplification.
A stone 石 on the left and the right side 㝵 (which looks like a barrier) together suggest a stone obstacle blocking the way.
For ガイ, imagine a guy tripping over a stone obstacle: guy -> ガイ, and the stone blocks his path.